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Abstract:
Kelvin waves are the most fundamental excitations of vortex flows, governing energy redistribution and stability in classical and quantum fluid dynamics. Despite their significance, the quantitative characterization of their dispersion relation and role in energy cascades remains a challenging problem, limited by experimental and theoretical constraints. Here, we investigate Kelvin wave propagation along a stable, controlled, and macroscopic vortex core, providing a comprehensive characterization of their dispersion relation, fully resolved in space and time, over a broad range of scales. In particular, we experimentally highlight helical bending modes and double-helix modes that confirm classical theoretical predictions. We also show how vortex local properties and mode structures influence the dynamics of Kelvin waves. Finally, we discuss some consequences of the reported statistics and dynamics of Kelvin waves on energy transfer processes and vortex stability in classical fluid mechanics, geophysical flows, and quantum hydrodynamics.